Wilson punctured network defects in 2D q-deformed Yang-Mills theory

TL;DR

This paper explores the properties of network defects in 2D q-deformed Yang-Mills theory, linking them to surface-line operators in 4D class S theories through skein relations and a new computational approach.

Contribution

It introduces a conjectural method to compute network defects in 2D q-deformed Yang-Mills theory using ideal triangulations and statistical mechanics.

Findings

Proposes skein relations for topological defects in 2D theories.

Links 2D defects to 4D surface-line operators via duality.

Suggests a new computational framework for defect analysis.

Abstract

In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU(N) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.